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Unifying controller Design for Stabilizing Nonlinear systems with Norm-Bounded control Inputs

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arXiv 2024年

作者： Li, Ming Sun, Zhiyong Weiland, Siep Control Systems Group Department of Electrical Engineering Eindhoven University of Technology Eindhoven5600MB Netherlands

This paper revisits a classical challenge in the design of stabilizing controllers for nonlinear systems with a norm-bounded input constraint. By extending Lin-Sontag’s universal formula and introducing a generic (state-dependent) scaling term, a unifying controller design method is proposed. The incorporation of this generic scaling term gives a unified controller and enables the derivation of alternative universal formulas with various favorable properties, which makes it suitable for tailored control designs to meet specific requirements and provides versatility across different control scenarios. Additionally, we present a constructive approach to determine the optimal scaling term, leading to an explicit solution to an optimization problem, named optimization-based universal formula. The resulting controller ensures asymptotic stability, satisfies a norm-bounded input constraint, and optimizes a predefined cost function. Finally, the essential properties of the unified controllers are analyzed, including smoothness, continuity at the origin, stability margin, and inverse optimality. Simulations validate the approach, showcasing its effectiveness in addressing a challenging stabilizing control problem of a nonlinear system. Copyright © 2024, The Authors. All rights reserved.

关键词： Nonlinear systems

Multivariable control of modular multilevel converters with convergence and safety guarantees

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arXiv 2024年

作者： Dreke, Victor Daniel Reyes Marca, Ygor Pereira Roes, Maurice Lazar, Mircea Control Systems Group Department of Electrical Engineering Eindhoven University of Technology Netherlands Electromechanics and Power Electronics Group Department of Electrical Engineering Eindhoven University of Technology Netherlands

Well-designed current control is a key factor in ensuring the efficient and safe operation of modular multilevel converters (MMCs). Even though this control problem involves multiple control objectives, conventional current control schemes are comprised of independently designed decoupled controllers, e.g., proportional-integral (PI) or proportional-resonant (PR). Due to the bilinearity of the MMC dynamics, tuning PI and PR controllers so that good performance and constraint satisfaction are guaranteed is quite challenging. This challenge becomes more relevant in an AC/AC MMC configuration due to the complexity of tracking the single-phase sinusoidal components of the MMC output. In this paper, we propose a method to design a multivariable controller, i.e., a static feedback gain, to regulate the MMC currents. We use a physics-informed transformation to model the MMC dynamics linearly and synthesise the proposed controller. We use this linear model to formulate a linear matrix inequality that computes a feedback gain that guarantees safe and effective operation, including (i) limited tracking error, (ii) stability, and (iii) meeting all constraints. To test the efficacy of our method, we examine its performance in a direct AC/AC MMC simulated in Simulink/PLECS and in a scaled-down AC/AC MMC prototype to investigate the ultra-fast charging of electric vehicles. Copyright © 2024, The Authors. All rights reserved.

关键词： Linear matrix inequalities

Equilibrium-Independent control of Continuous-Time Nonlinear systems via the LPV Framework - Extended Version

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arXiv 2023年

作者： Koelewijn, Patrick J.W. Weiland, Siep Tóth, Roland The Control Systems Group Department of Electrical Engineering Eindhoven University of Technology Eindhoven Netherlands The Systems and Control Laboratory Institute for Computer Science and Control Budapest Hungary

In this paper, we consider the analysis and control of continuous-time nonlinear systems to ensure universal shifted stability and performance, i.e., stability and performance w.r.t. each forced equilibrium point of the system. This "equilibrium-free" concept is especially beneficial for control problems that require the tracking of setpoints and rejection of persistent disturbances, such as input loads. In this paper, we show how the velocity form, i.e., the time-differentiated dynamics of the system, plays a crucial role in characterizing these properties and how the analysis of it can be solved by the application of Linear Parameter-Varying (LPV) methods in a computationally efficient manner. Furthermore, by leveraging the properties of the velocity form and the LPV framework, a novel controller synthesis method is presented which ensures closed-loop universal shifted stability and performance. The proposed controller design is verified in a simulation study and also experimentally on a real system. Additionally, we compare the proposed method to a standard LPV control design, demonstrating the improved stability and performance guarantees of the new approach. Copyright © 2023, The Authors. All rights reserved.

关键词： controllers

Modular ISRU systems as a Building Block for Sustainable Space Exploration 73

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Modular ISRU Systems as a Building Block for Sustainable Spa...

73rd International Astronautical Congress, IAC 2022

作者： Fälker, Svenja Dorau, Tim Viedt, Isabell Mädler, Jonathan Urbas, Leon Tajmar, Martin Bach, Christian Institute of Aerospace Engineering Space Systems TU Dresden Marschnerstraße 32 Dresden01307 Germany Institute of Automation Process Control Systems and Process Systems Engineering Group TU Dresden Helmholtzstraße 14 Dresden01069 Germany

Leading space agencies and companies identified the utilization of local resources as foundation for the continuous long-term exploration of the solar system within the Global Exploration Roadmap. In-Situ Resource Utilization (ISRU) will be one of the key technologies for sustainable space exploration and habitation missions to Moon, Mars and beyond. Defined production systems based on hydrogen value chains are utilized as essential building blocks to transform the available resources into valuable elements for energy, propulsion, life support or production systems. The current research at TU Dresden addresses the engineering of ISRU systems using a modular plant concept of standardized, interchangeable and reusable modules. The development, production and automation processes are defined based on the existing standards on modular process plants (VDI 2776) and modular automation (VDI/VDE/NAMUR 2658) for terrestrial application. Therein, a module called Process Equipment Assembly (PEA) realizes unit operations which are interconnected to form different plant configurations that enable flexible production paths. These standardized architectures and concepts are adapted to the requirements of space utilization. Compared to currently developed highly specialized single use systems, a modular plant approach according to these standards allows the flexible application to different mission requirements and environmental conditions. In advance, modular plants minimize the development effort and risk, lead to a lowered market entry threshold for small and medium-sized enterprises from diverse market sectors and encourage commercial competition between manufacturers. This paper includes initial research work as a foundation for the future development process of modular ISRU process plants. A major input for the holistic development of modular ISRU plants are top-level mission characteristics and derived sub-level requirements. They represent a valuable input for the developme

关键词： Computer software reusability

Hydrodynamic and Static Stability Analysis of a Hybrid Offshore Wind-Wave Energy Generation: An Expansion of Semisubmersible Floating Wind Turbine Concept 15th

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Hydrodynamic and Static Stability Analysis of a Hybrid Offsh...

15th European Wave and Tidal Energy Conference, EWTEC 2023

作者： Aboutalebi, Payam Garrido, Aitor J. Garrido, Izaskun Nguyen, Dong Trong Gao, Zhen Department of Marine Technology Trondheim7491 Norway Automatic Control Group–ACG Institute of Research and Development of Processes–IIDP Department of Automatic Control and Systems Engineering Faculty of Engineering of Bilbao University of the Basque Country–UPV/EHU Spain School of Naval Architecture Ocean and Civil Engineering Shanghai Jiao Tong University Shanghai200240 China

Marine structures like Floating Wind Turbine (FWT) is exposed to the oncoming waves and wind that can cause oscillatory motions within the system. These undesired oscillations can have negative impacts on the efficiency of the system, reduce its lifespan, hinder energy extraction, increase stress levels, and raise maintenance costs. To mitigate these negative impacts, the integration of Wave Energy Converters (WECs) into the FWT system has been proposed. This hybrid system may be capable of extracting coupled wind-wave energy and transferring electrical power to the shared grid. This paper presents an investigation of the use of Oscillating Water Columns (OWCs), a type of WECs, within a FWT system. The purpose of using an OWC is to increase the hydrodynamic damping and reduce the resonant motions of the floating wind turbines under environmental loads, including both wind and wave loads. This is because the wave energy from OWC would be very small as compared to the wind energy. However, OWCs can provide a damping source for reducing the resonant motions of the floater, especially the pitch resonant motions. This would be very beneficial for the power performance of the floating w ind turbine and the structural design of the floater. T he p urpose of this paper is to redesign the original FWT platform to accommodate the additional OWCs by considering the hydrostatic stability and hydrodynamics since the new elements, the OWCs, can significantly change the response of the platform. The redesign of the original FWT involves the integration of OWCs within two out of three columns of an existing semisubmersible platform for a 12 MW FWT. To do this, two moonpools, which are consistent with OWC air chambers, have been created within two columns of the FWT. The water ballast was designed for the columns with and without OWCs. After that the redesign is done hydrostatic stability and hydrodynamics analyses are evaluated. The hydrodynamics properties are discussed in terms o

关键词： Tidal power

Optimal Stopping Problems in Low-Dimensional Feature Spaces: Lossless Conditions and Approximations

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Optimal Stopping Problems in Low-Dimensional Feature Spaces:...

IEEE Conference on Decision and control

作者： M.J.T.C. van Zutphen W.P.M.H. Heemels D.J. Antunes Department of Mechanical Engineering Control Systems Technology Group Eindhoven University of Technology The Netherlands

Optimal control problems can be solved by dy-namic programming. However, this method suffers from the curse of dimensionality. To resolve this, simplified versions of the original problem are often constructed in lower-dimensional feature spaces, leading to approximate policies. Yet, the connections between the original and the approximate policy and costs are rarely formalized. This paper addresses this challenge for optimal stopping problems. We start by providing conditions for lossless feature representations. This means that from an optimal policy obtained in feature space, an optimal policy in the original space can be constructed. Then, we search for modified versions of the original problem that (i) admit a lossless feature representation of far lower dimension; and (ii) provide upper and lower bounds on the optimal cost of the original problem. We can then use policies obtained in feature space using these modified problems to provide approximate policies for the original problem that are guaranteed to perform better than or equal to this aforementioned cost upper bound. We apply our tools in a high-dimensional precision farming intervention problem, where our tools allow for a dramatic decrease in complexity with only a small increase in the cost.

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A time-varying matrix solution to the Brockett decentralized stabilization problem

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arXiv 2023年

作者： Sun, Zhiyong Control Systems Group Department of Electrical Engineering Eindhoven University of Technology Eindhoven Netherlands

This paper proposes a time-varying matrix solution to the Brockett stabilization problem. The key matrix condition shows that if the system matrix product CB is a Hurwitz H-matrix, then there exists a time-varying diagonal gain matrix K(t) such that the closed-loop minimum-phase linear system with decentralized output feedback is exponentially convergent. The proposed solution involves several analysis tools such as diagonal stabilization properties of special matrices, stability conditions of diagonal-dominant linear systems, and solution bounds of linear time-varying integro-differential systems. A review of other solutions to the general Brockett stabilization problem (for a general unstructured time-varying gain matrix K(t)) and a comparison study are also provided. Copyright © 2023, The Authors. All rights reserved.

关键词： Linear systems

Adaptive identification of SISO linear infinite-dimensional systems

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arXiv 2023年

作者： Chattopadhyay, Sudipta Sukumar, Srikant Natarajan, Vivek The Systems and Control Engineering Group Indian Institute of Technology Bombay Mumbai400076 India

We propose an adaptive algorithm for identifying the unknown parameter in a linear exponentially stable single-input single-output infinite-dimensional system. We assume that the transfer function of the infinite-dimensional system can be expressed as a ratio of two infinite series in s (the Laplace variable). We also assume that certain identifiability conditions, which include a persistency of excitation condition, hold. For a fixed integer n, we propose an update law driven by real-time input-output data for estimating the first n + 1 coefficients in the numerator and the denominator of the transfer function. We show that the estimates for the transfer function coefficients generated by the update law are close to the true values at large times provided n is sufficiently large (the estimates converge to the true values as time and n tend to infinity). The unknown parameter can be reconstructed using the transfer function coefficient estimates obtained with n large and the algebraic expressions relating the transfer function coefficients to the unknown parameter. We also provide a numerical scheme for verifying the identifiability conditions and for choosing n sufficiently large so that the value of the reconstructed parameter is close to the true value. The class of systems to which our approach is applicable includes many partial differential equations with constant/spatially-varying coefficients and distributed/boundary input and output. We illustrate the efficacy of our approach using three examples: a delay system with four unknown scalars, a 1D heat equation with two unknown scalars and a 1D wave equation with an unknown spatially-varying coefficient. Copyright © 2023, The Authors. All rights reserved.

关键词： Partial differential equations

Complexity-Bounded Relaxed Dynamic Programming

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Complexity-Bounded Relaxed Dynamic Programming

IEEE Conference on Decision and control

作者： R.M. Beumer M.J.G. Van De Molengraft D.J. Antunes Department of Mechanical Engineering Control Systems Technology Group Eindhoven University of Technology The Netherlands

The idea behind relaxed dynamic programming for optimal control problems is to settle with a suboptimal but simpler control policy that guarantees a cost within a fixed constant factor from the optimal cost. Such a policy results from parameterized approximate value functions and the complexity of these functions determines the complexity of the policy. Typically, the more stringent the constant factor from the optimal cost is, the larger the complexity. However, relaxed dynamic programming does not give any guarantees on the complexity, which might still be unpractical. To tackle this issue, we propose to rather find the best factor away from optimality for a given complexity bound. We consider a large class of problems where the value functions can be represented as the minimum of quadratic functions. For this class, we propose a modified relaxed dynamic programming algorithm that ensures bounded complexity while still providing tight cost guarantees. A crucial step in the algorithm is the search for the best cost factor for a given policy with desired complexity, shown to be an optimization problem subject to Linear Matrix Inequalities (LMIs). We provide a new subclass of problems within this class and illustrate the effectiveness of our policy in a numerical instance of this subclass.

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